The generation of high resolution, large field of view images is important in many areas, such as virtual reality, computer vision, robotic navigation and the like. It is generally known that mosaic images can be computed by stitching together multiple images, where the individual images correspond to different views of the same scene. Generally, the different views have approximately the same viewpoint but correspond to different sections of the scene of interest. A variety of techniques for image mosaicing are known. Such techniques generally employ an imaging system that uses a conventional imaging lens to form an image of the scene. A problem with conventional lenses is that they are limited in their fields of view in both image directions. Therefore, to construct a panorama or a complete spherical image, a large number of images need to be captured and processed. In addition, to capture a complete spherical view the imaging systems need to scan the scene in three dimensions without missing any substantial areas. This is difficult to accomplish using conventional camera systems.
An alternate approach is to use a wide angle lens such as a fish eye lens. This approach reduces the number of images since the field of view captured in each image is significantly larger than in the case of conventional images. However, when a fish eye lens is used, the resolution of the image is uniformly distributed over the increased field of view and as a result, such systems are not well suited for high resolution mosaicing.
Catadioptric imaging systems which use a combination of mirrors and lenses to form an image are also known. The use of mirrors provides the designer great flexibility in terms of manipulating the field of view and resolution characteristic of the imaging system. Catadioptric systems have shown promise for wide angle imaging.
Despite their known benefits, known catadioptric imaging systems cannot capture a complete spherical view within a single image. The field of view is typically limited by two factors, namely, a blindspot that results from the mirror (or mirrors) seeing the camera itself and the finite extent of the mirror (or mirrors) that corresponds to a truncation of the field of view. Furthermore, as the field of view of a catadioptric system is increased, such as by increasing the extent of the imaging mirrors, the resolution of the image is naturally reduced. This is because in any given image detector (CCD, film, etc.) the number of picture elements is fixed and an increase in the field of view corresponds to each pixel subtending a larger solid angle with respect to the captured scene.
Several variations of wide angle imaging systems are known. As shown in FIG. 2, a first system includes an image sensor 202, an objective (imaging) lens 204 and a curved (convex or concave) mirror 206. The curved mirror 206 can have a variety of shapes. In the case of a hyperboloidal mirror, if the entrance pupil of the imaging lens is placed at the external (far) focus F′1 of the mirror 206, only the scene rays that approach the near focus F1 of the mirror 206 are imaged by the system. In this case, the near focus of the mirror is the center of projection of the complete catadioptric system.
More compact catadioptric designs are possible using the concept of optical folding which uses multiple mirrors. As shown in FIG. 3, the near focus F2 of the secondary mirror 302 is made to coincide with the far focus F′1 of the primary mirror 304. Then, if the entrance pupil P of the imaging lens 306 is placed at the far focus F′2 of secondary mirror 302, the imaging system captures only those scene rays that approach the near focus F1 of the primary mirror 304, making it the center of projection of the complete imaging system.
A variety of mirror configurations may be used is catadioptric systems, with the mirror shapes being hyperboloidal, ellipsoidal, and paraboloidal. If the requirement that the center of projection should be a single point is relaxed, a variety of other shapes can also be used, such as spherical and conical. In fact, the mirror profiles are not confined to first order or second order profiles but can be higher order polynomials that permit the manipulation of the resolution characteristics of the imaging system.
Catadioptric imaging systems include one or more curved mirrors in the imaging system and the mirrors may be concave or convex. In the case of multiple mirrors, there is at least one curved mirror and one or more of the others could be planar mirrors.
Another embodiment of a catadioptric imaging system is illustrated in FIG. 4. This system includes a parabolic mirror 401, a relay lens 404, an imaging lens 406 and an image detector 408. The relay lens 404 is typically an achromatic lens with a short focal length. The distances between the relay lens 404, the imaging lens 406 and the parabolic mirror 402 are chosen such that only principal rays of light that are orthographically reflected by the parabolic mirror are imaged by the system. These reflected rays correspond to scene rays that approach the focus of the parabola.
Typically, the image captured using a wide angle catadioptric system looks like that illustrated in FIG. 5. This image is donut shaped and has two circles that are of the limits of the imaging system's field of view. The first inner circle B′corresponds to the blindspot that is caused by the primary mirror being obstructed in its view by other mirrors, the imaging lens, or detector. The second (outer) circle L′ of the field of view results from the finite extent of the mirrors. As can be seen, such a field of view is 360 degrees in one dimension and less than 180 degrees in the other. It should be noted that the imaging lens and detector need not necessary be used to image the complete field of view captured by the mirrors. Instead, they may be used to image a smaller section of the donut image in order to increases image resolution (lower the solid angle imaged by each pixel).